Asymptotic properties of a random graph with duplications

Abstract

We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an almost surely asymptotic degree distribution, with stretched exponential decay; more precisely, the proportion of vertices of degree d tends to some positive number c _d > 0 almost surely as the number of steps goes to ∞, and c _d ~ (eπ) ^1/2 d ^1/4e ^{-2√ d} holds as d → ∞.